At 8 a.m. the race hadn’t started.
Presumably this was said soemtiems after 8 am, when the action was already in the past.
When I arrived at 11.30 a.m., the competition had begun.
This would have been written at some later time, when 11:30 was already in the past.
At time T, X had started.
The4 start is in the past of T, and T is in the past of the4 speaker/writer. so this "had" form, the past perfect, is used to show a sequence of events, all of which are in the past. First came the start, then came T, and later yet the present in which the speaker describes these events.
At time T, X had not begun.
Again a past sequence is begin shown. during the priod before T, X did not stsart. Then came T, and finally the speaker's present.
The past perfect is used for these situations.
This Your Dictionary article descries the past perfect and its uses.